IP AMaths Notes (Upper Sec, Year 3-4): 16) Applications of Differentiation
In one line
Tangents, normals, stationary points, and related rates in IP AMaths.
Last updated 30 Nov 2025
Want small-group support? Browse our IP Maths Tuition hub. Not sure which level to start with? Visit Maths Tuition Singapore.
Planning a revision session? Use our study places near me map to find libraries, community study rooms, and late-night spots.
Read in layers
1 second
Read the summary above.
10 seconds
Scan the first few sections below.
100 seconds
Jump into the section that matches your decision.
- Start Here
- 1 Common tasks
- 2 Worked example - Tangent and normal
- 3 Worked example - Optimisation
Q: What does IP AMaths Notes (Upper Sec, Year 3-4): 16) Applications of Differentiation cover?
A: Tangents, normals, stationary points, and related rates in IP AMaths.
Apply derivatives to describe gradient, optimise functions, and connect rates.
Keep the full topic roadmap handy via our IP Maths tuition hub so you can jump into related drills, quizzes, or diagnostics as you move through these notes.
New to the Integrated Programme? Start with What is IP? | Browse all free IP notes.
Applications here match the SEAB GCE O-Level Additional Mathematics (4049) requirements: tangents/normals, stationary points with second-derivative tests or sign charts, simple optimisation, and related rates in radians.
Status: SEAB O-Level Additional Mathematics 4049 syllabus (exams from 2025) checked 2025-11-30 - scope unchanged; remains the reference for this note.
Start Here
| Read time | What to take away |
| 1 second | Applications of differentiation turn gradients into decisions. |
| 10 seconds | Use derivatives to find tangent gradients, normal gradients, stationary points, and related rates. Always classify stationary points before naming a maximum or minimum. |
| 100 seconds | Example: if y' = 0 at x = 3, test the second derivative or a sign chart before calling it a turning point. If y'' is positive, it is a local minimum. |
1 Common tasks
- Tangent gradient at
